Zack Greinke of the Milwaukee Brewers pitches against the Pirates at Miller Park on Friday.

Zack Greinke of the Milwaukee Brewers pitches against the Pirates at Miller Park on Friday. (Mark Hirsch/Getty Images)

There is a rumor the White Sox are interested in trading for Milwaukee starter Zach Greinke. I believe the rumor was started by Gavin Floyd’s right forearm, the one with tendinitis that likely will land him on the disabled list and scream for the White Sox to trade for a starter.

Or maybe the rumor was first whispered by John Danks’ seemingly hopeless shoulder pain, which isn’t really that hopeless, but it has left the Sox helpless since, I don’t know, opening day. Something like that.

And then there was Leyson Septimo’s miserable performance in the eighth inning in Boston on Monday night. The Sox got a gutsy performance from Dylan Axelrod, the usual suspect in the Sox’s seasonlong game of starter roulette. Axelrod held the Red Sox to one run in 6 2/3 innings, but then the left-handed Septimo went walk, walk, homer against three straight left-handed hitters. Ballgame, buh-bye, scream for a veteran set-up man while you’re screaming for a reliable starter.

Point is, Ken Williams needs to make some deals. Not just because the Tigers overtook Indians for second place in the AL Central, but because Williams’ Sox are the suprising division leaders.

Let’s be honest: It doesn’t take much to convince Williams to make a deal. He doesn’t like to wait -- see the Kevin Youkilis steal for details -- and making only one trade a month is totally unsatisfactory for him.

His bullpen consists of Matt Thornton and six rookies with more rookies replacing bad rookies.

Question also is, what does Williams have to trade?

Because Williams apparently gets paid on commission, he already has dealt away a lot of prospects. To his credit, and to that of the Sox’s development system, Williams has stocked his big-league team with an unbelievable number of young, power arms. If Williams doesn’t want to move anybody out of his first-place clubhouse, then he would need a lot of good prospects, or a lot of players that at least one team considers good prospects.

But here’s the thing: The Sox’s rumored interest in Greinke plays to a team that isn’t loaded with top minor-league prospects, and here’s why: The Brewers have limited trading partners because of Greinke’s well-documented issues with social anxiety disorder.

The Yankees, Dodgers, Red Sox --- all the big-city teams --- reportedly ignored Greinke because of that. Finally, the Sox’s small-market mentality was becoming an advantage, no matter that the Sox play in Chicago, which, at last look, was regarded as a big city by some. The Sox don’t draw the way first-place teams should, and as recently as Monday afternoon, Kevin Youkilis was expressing the joy of playing in the drama-free environment of the South Side because the Sox “play second fiddle to the Cubs.’’ Those factors helped create a good spot for Williams to make a big move.

And then of course, something goes wrong.

The Brewers will skip Greinke’s next start after he pitched horribly in three consecutive starts, and I mean three consecutive starts. Greinke pitched on the Saturday before the All-Star Break, but was ejected in the first inning. Then he volunteered to pitch the next day, and was rocked over three innings. Then he started the first game after the All-Star break, and stunk again.

I don’t know if the Sox were going to be at Miller Park on Wednesday when Greinke was scheduled to start against St. Louis, but forget it. The Brewers are skipping a complete turn through the rotation to give Greinke a chance to return to a normal routine. He won’t pitch again until next Tuesday and would be on track to pitch once more before the non-waiver trade deadline July 31.

When you look at who’s selling and who’s buying, the sellers have a lot of leverage because of the new second wild-card berth. More teams think they’re in it, or at least try to sucker their fans into believing it. (Sorry, Oakland.) If the Sox are going to buy, they need to find a spot to minimize that leverage the way they did with Boston giving away Youkilis. That’s the only way the Sox can get a reliable starter. They certainly can’t fade the leverage and the competition of big-boy buyers in New York, Boston and Los Angeles.

Compared to what the Cubs figure to get for Ryan Dempster and Matt Garza, Greinke seems like the answer for the Sox. Cole Hamels might or might not come on the market. Same goes for Cliff Lee. Either one sounds like a New York-Boston bidding war. In fact, I think ESPN plans to televise Yankees-Red Sox trade battles.

And another thing: The Sox have to love the idea that Greinke’s contract expires after this season. He would have millions of dollars worth of reasons to pitch well.

Greinke still might be the answer for the Sox. I expect Williams to acquire at least one veteran reliever, some way, somehow, even if Jesse Crain comes back strong. I also expect the Sox GM to come up with a rental starter.

And you know what? The more I think about Williams’ gambling nature, the more I believe he might be pleased that Milwaukee’s limited trade partners are suddenly matched by Greinke’s limited auditions leading up to the deadline. I mean, Williams has seen enough of the former Royal already, and Greinke fits Williams’ trade-deadline pattern of acquiring big names he believes are worth a three-month gamble.

Greinke-to-the-Sox might not happen, but that’s still the way I’d bet.